The ratio of the masses of two circular rings | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The moment of inertia $I$ of a circular ring about its central axis is given by $I = MR^2$,where $M$ is the mass and $R$ is the radius.Since the r

Vedclass · Accepted Answer

$2:1$

Vedclass · Answer

(B) The moment of inertia $I$ of a circular ring about its central axis is given by $I = MR^2$,where $M$ is the mass and $R$ is the radius.Since the ratio of diameters is $2:1$,the ratio of radii $R_1/R_2$ is also $2:1$.Given $M_1/M_2 = 1/2$ and $R_1/R_2 = 2/1$.The ratio of moments of inertia is $\frac{I_1}{I_2} = \frac{M_1 R_1^2}{M_2 R_2^2} = \left( \frac{M_1}{M_2} ight) \left( \frac{R_1}{R_2} ight)^2$.Substituting the values: $\frac{I_1}{I_2} = \left( \frac{1}{2} ight) 	imes \left( \frac{2}{1} ight)^2 = \frac{1}{2} 	imes 4 = 2$.Thus,the ratio is $2:1$.

The ratio of the masses of two circular rings is $1:2$ and the ratio of their diameters is $2:1$. The ratio of their moments of inertia is:

Similar Questions

Why does a solid sphere have a smaller moment of inertia than a hollow cylinder of the same mass and radius,about an axis passing through their axes of symmetry?

If the radius of a solid sphere is doubled while keeping its mass constant,what is the ratio of its moment of inertia about any of its diameters?

Two rings have their masses in ratio $1 : 2$ and their diameters are in the ratio $2 : 1$. The ratio of their moments of inertia is

Two half rings are joined as shown in the figure. Each half ring has a radius $R$ and mass $M$. The moment of inertia of the system about the axis $XX'$ is

$A$ circular disc is to be made by using iron and aluminium,so that it acquires maximum moment of inertia about its geometrical axis. This is possible with:

Vedclass Test Series

Exam Paper Generator

Online Exam Module